RSA 159:6 II. No photograph or fingerprint shall be required or used as a basis to grant, deny, or renew a license to carry for a resident or nonresident, unless requested by the applicant.
My bad. No Photo required. If they denied, get them to write a letter as to why they are denying you a license (as per 159:6 part I - The license shall be issued within 14 days after application, and, if such application is denied, the reason for such denial shall be stated in writing, the original of which such writing shall be delivered to the applicant, and a copy kept in the office of the person to whom the application was made. )
Good luck!